Electrostatic Potential and Capacitance
- Define electric potential at a point.
It is defined as the amount of work done in bringing a unit test charge from infinity to that point in the electric field.
- Define potential difference?
It is defined as the work done in moving a unit test charge from one point to another in the electric field.
- Define equipotential surface.
It is defined as the surface at which electric potential is same at all points.
It is a surface obtained by joining all those points at which the electric potential is same.
- How much work is done in movings 500 pC charge between two points on an equipotential surface?
Since the potential difference between two given points on the equipotential surface is zero, hence work done is zero.
- Why both electric potential and electric potential difference are scalar quantities?
We know that electric potential and potential differece = Work / AS Charge work and charge both are scalar quantities, so both electric charge
potential and electric potential difference are scalar quantities.
- Does the work done in moving a test charge in an electric field depend upon the path followed between two points? Then on what factors it depends?
work done in moving a test charge does not depend upon the nature of path followed between two points in an electric field but it depends upon the initial and final positions of the path followed.
- Define one electron volt (1 eV). Give its value.
It is defined as the energy acquired by an electron on applying a potential difference of one volt across it.
1eV = 1.6 x 10-19J.
- Do electrons tend to go to regions of high positive potential or low potential? Why?
The electrons tend to go to a region of high potential because they carry negative charge.
- Why a man inside an insulated metallic cage does not receive a shock, when the cage is highly charged?
A man inside an insulated metallic cage does not recieve a shock as the circuit between him and the cage is not complete, so no current will pass through the body of the man. Hence he will not receive any shock.
- What will be the work done in moving a charge of + 5 μC on the surface of a spherical shell of radius 10 cm having +1μC charge at its centre through a distance of 5 cm?
Zero, because all points on the circular path along the surface of the shell are at the same potential.
- Can we have non-zero electric potential in the space, where electric field strength is zero? Explain.
Yes. We know that E =dV/dr
when E = 0, dV = 0 or V = constant (non-zero).
- Electric field is geometrically represented by the lines of force How do we represent the electric potential geometrically?
Electric potential is geometrically represented by equipotential surtax.
- Does the positive or negative nature of electric potential depend upon the nature of test charge? Explain.
No. It does not depend upon the nature of test charge but ‘ certainly depends on the nature of source charge.
- Explain that the potential is the degree of electrification of a body.
We know that V q. V increases with the increase of charge on the body. Thus a body at higher potential possesses more charge than when it is at lower potential. Hence potential is the degree of electrification of a body.
- Define capacitance. What is its S.I. unit?
It is defined as the ability of a conductor to store charge. It is also defined as the ratio of electric charge on it to its electric potential. S.I. unit of capacitance is farad (F).
- Why electrical conductivity of earth’s atmosphere increases with altitude?
The ionization of atmosphere increases with height. Thus due to increase of ionization, conductivity of atmosphere increases.
- What do you mean by equivalent capacitor?
A combination of capacitors in an electric circuit can be replaced by a single capacitor that has the same capacitance as the actual combination of the capacitors. Such a capacitor is called equivalent capacitor.
- Can we give any desired amount of charge to a capacitor? Explain.
No. The maximum charge that can be given to a capacitor is limited by the dielectric strength of the medium between the two plates of the capacitor.
- Why is a parallel plate capacitor named so?
It is named so because it is made of two parallel conducting plates placed parallel to each other.
- In what form is the energy stored in a charged capacitor?
The energy is stored in the form of electric field between the two plates i.e., in the form of electric energy in a charged capacitor.
- Define dielectric strength of the medium.
It is defined as the maximum value of electric field that a dielecric can with stand, without the break down of the dielectric.
- Define dielectric constant of a medium in forms of the capacitance of the capacitor.
It is defined as the ratio of the capacitance of capacitor with a dielectric medium between its plates to its capacitance with air between the plates. Eg.
K = C/C0
- Why the Van-de-Graff generator is enclosed inside an earth connected steel tank filled with air under pressure?
It is done to prevent the leakage of charge due to ionisation of air surrounding the large shell because of very high voltage of the generator. The air under pressure, as soon as free ions are produced, they recombine to form neutral air molecules.
- The dielectric constant of a conductor can be taken to be infinitely large, infinitely small or optimum. Which of the three alternatives is correct?
When a conductor is placed inside an electric field, the field lines inside the conductor become zero. The dielectric constant which is the ratio of the strength of applied electric field to the reduced value of electric field ((K=E0/E) will be infinate as E = 0
- An uncharged insulated conductor A is brought near a charged insulated conductor B. What happens to charge and potential
The charge on conductor B remains the same, but its potential gets lowered.
- How does a dielectric differ from an insulator?
Both the dielectrics and insulators cannot conduct electricity. But in case of dielectric, when an external electric field is applied, induced charges appear on the faces of the dielectric. In other words, the d ielectrics have the property of transmitting electric effects without conducting.
- What will be the effect of introducing a dielectric medium having dielectric consant K between the plate of a parallel plate capacitor on:
(a) the charge on the plates
(b) potentials difference between the plates
(c) electric field between the plates
(d) capacitance of capacitor
(e) electrostatic energy (v) stored in the capacitor.
(a) Charge on plates remains same.
(b) Potential difference between the plates decreases as V = E x d and E decreases.
(c) Electric field between the plates decreases.
(d) Capacitance (C = q/V ) increases on introduction of dielectric medium between the plates.
(e) U = 1/2 qV as U ∝ V, so U also decreases.
- Name three polar and three non-polar molecules.
HCl, H2O and NH3 are three polar molecules while N2, O2 and CH4 are non-polar molecules.
- What do you mean by saying that electrostatic field in conservative in nature?
An electric field is said to be conservative if :
(i) Line integral of electric field between two given points is independent of the nature of path followed.
(ii) Line integral of electric field along a closed path is zero.
- What are properties of equipotential surfaces?
Following are the properties of equipotential surfaces:
(i) No work is done in moving a test charge over an equipotential surface from one point to another.
(ii) The electric field is always perpendicular to the equipotential surface.
(iii) The equipotential surfaces help us to distinguish regions of strong field from those of weak field.
(iv) The equipotential surfaces tell us the direchon of electric field. – (v) No two equipotential surfaces intersect each other.
- Define polarisation.
It is defined as the process of stretching of dielectric atoms due to the displacement of charges in the atoms under the action of applied electric field. This stretching of atoms continues till the restoring force becomes just equal and opposite to the force exerted by the applied electric field on the charges. Thus C.G. of + ve nucleus does not coincide with the C.G. of electrons that are – vely charged due to this stretching and the atom thus acquires a dipole moment.
- Define capacitor.
A capacitor is a device used for storing large quantity of charge. A given conductor cannot be charged to any extent. After certain limit, change given to the conductor leakes away into the atmosphere. Capacity of a given conductor is a limit to which it can acquire charge. Capacitor or condensor is an arrangement of conductors by which capacity of a given conductor can be increased.
- An electric dipole consists of two opposite charges each of 1 μC separated by 2 cm. The dipole is placed in an external uniform field of 105NC-1 Find the work done in rotating the dipole through 180° starting from its initially aligned position.
Here, q = 1 μC = 1 x 10-6C
2a = dipole
length = 2 cm = 2 x 10-2 m.
θ = 0°, θ2 = 180°, E = 105 NC-1.
.’. p = 2aq = 2 x 10-2 x 10-6 = 2 x 10-8 cm.
W = work done = ?
Using the relation
W- = pE (cosθ1 – cosθ2)
= 2 x 10-8 x 105 (cos 0 – cos 180)
= 2 x 10-3[1 – (- 1)]
= 2x 10-3 x 2 = 4 x 10-3 J
= 0.004 J.
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